A theory is presented which explains the observed birefringence of colloidal dispersions of fine magnetic particles. The system is assumed to consist of pairs of interacting particles, interactions between pairs being negligible. A pair of particles approximates to a single particle with a high degree of optical anisotropy. Application of a magnetic field to the colloid has the effect of aligning the axes of the pairs, resulting in the measured birefringence. On the basis of this model, the birefringence of a magnetic colloid is calculated. The form of the numerical results is consistent with experimental data. In particular it is shown that in small fields the birefringence is proportional to H2.